List of top Mathematics Questions

If two dice are thrown simultaneously, then the probability that the sum of the numbers which come up on the dice to be more than $5$ is

If $Z = \frac {(\sqrt {3}+ i)^3 (3i+4)^2}{{(8+6i)^2}}$ then $|Z|$ is equal to

If $\begin{vmatrix} {2a}&{x_1} &{y_1}\\ {2b}&{x_2}& {y_2} \\ {2c}&{x_3}&{y_3}\\ \end{vmatrix}$ $ = $$\frac {abc}{2} \neq 0$, then the area of the triangle whose vertices are $(\frac {x_1}{a},\frac {y_1}{a})$$(\frac {x_2}{b},\frac {y_2}{b})$$(\frac {x_3}{c},\frac {y_3}{c})$ is

The sum of first 9 terms of the series $ \frac{1^3}{1} + \frac{1^3+2^3}{1+3} + \frac{1^3+2^3+3^3}{1+3+5} +...$ is

A man takes a step forward with probability $0.4$ and one step backward with probability $0.6$, then the probability that at the end of eleven steps he is one step away from the starting point is

Find the maximum value of $|z|$ when $\left|z-\frac{3}{2}\right|=2, z$ being a complex number.

Let  \(f(x) = \begin{cases} \frac{x^3+x^2-16x+20}{(x-2)^2} & if x \neq 2 \\ b & \text{if x = 2} \end{cases}\)  If \(f(x)\) is continuous for all \(x\) , then \(b\) is equal to

The number of equivalence relations on the set {1, 2, 3} containing (1, 2) and (2,1) is

Let $ A = \left\{x\in R; x\ge\frac{1}{2}\right\} $ and $ B = \left\{x\in R; x\ge\frac{3}{4}\right\} $ If $ f : A \rightarrow B $ is defined as $ f(x) = x^2 - x + 1 $ , then the solution set of the equation $ f(x) = f^{-1}(x) $ is

Let $f\left(x\right) = sin\left(\frac{\pi}{6}sin\left(\frac{\pi}{2}sin\,x\right)\right)$ for all $x \in R$ and $g\left(x\right) = \frac{\pi}{2}$ $sin\, x$ for all $x \in R$. Let $(fog) (x)$ denote $f(g(x))$ and $(gof) (x)$ denote $g(f(x))$. Then which of the following is (are) true ?

$ Let \,A = [a_{ij}]_{mxn} $ be a matrix such that $ a_{ij} = 1,\forall $ $ i,j. $ Then,

Which of the following values of $\alpha$ satisfy the equation. $\begin{vmatrix}\left(1+\alpha\right)^{2}&\left(1+2\alpha \right)^{2}&\left(1+3\alpha \right)^{2}\\ \left(2+\alpha \right)^{2}&\left(2+2\alpha \right)^{2}&\left(2+3\alpha \right)^{2}\\ \left(3+\alpha \right)^{2}&\left(3+2\alpha \right)^{2}&\left(3+3\alpha \right)^{2}\end{vmatrix} = -648\alpha ?$

Three dice are rolled once. The chance of getting a score of $5$ is

The number of solutions of the equation $\left|cot\,x\right|=cot\,x+\frac{1}{sin\,x}, \left(0 \le x \le 2\pi\right)$ is

The solution of differential equation $x \frac {dy}{dx}+2y=x^2$ is

The set of values of $ x $ for which $ \frac{tan 3x - tan 2x}{1+ tan 3x\,tan2x} = 1 $ is

Let P and Q be distinct points on the parabola $y^2 = 2x$ such that a circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle $?OPQ$ is $3\sqrt{2},$ then which of the following is (are) the coordinates of P ?

The sum of the common roots of the equations , $ {{x}^{3}}+2{{x}^{2}}-5x+2=0~ $ and $ {{x}^{3}}+\text{ }{{x}^{2}}-8x+4=0, $ is

$\frac{\sin x - \sin 3x}{\sin^{2} x -\cos^{2} x}$ is equal to

In a $\Delta ABC, cosec\, A(\sin\, B \, \cos\, C + \cos \, B\, \sin\, C)$ =

The number of real solutions of the equation $(\sin x-x)\left(\cos x-x^{2}\right)=0$ is